Semi-empirical model for depth dose distributions of megavoltage x-ray beams

The dose distribution due to absorption of photon energy fluence in a homogeneous water phantom irradiated by megavoltage x-ray beams has been analyzed with a semiempirical model. The method generalizes an analytical formalism for the scattering component of dose within a water phantom which was developed recently for monoenergetic photon beams. Contributions to dose via Compton interaction and pair creation form the essential structure of the secondary component formula. Both the central-axis percent depth dose and off-central-axis ratios can be determined for beams of different sizes, used at any value of source to surface distance. The input data include the values of linear attenuation and energy-absorption coefficients in water at energies between 10 keV and the equivalent energy of the beam. Predicted values of the central-axis percent depth dose and the off-central-axis ratios are compared with the measured data for 2, 4, 6, 8, 10, 14, 20, 35, 45, and 70 MVp x-ray beams. For the central-axis percent depth dose, agreement is within 3% for fields of sizes between 5 X 5 and 20 X 20 cm2, and 5% for larger fields, for beams of MVp up to 20. For higher energy beams, comparison was made only for the 10 X 10 cm2 fields and the discrepancies were within 3%. For the off-central-axis ratios, agreement between the predicted and measured values is within 5% over the umbra region but worsens in the penumbra region and geometrical shadow. This formalism requires large computer storage for generating data for all realistic beams irradiating normal-size phantoms.